Problem: If $x \dagger y = 2x-8y$ and $x \barwedge y = 3x-5$, find $0 \barwedge (0 \dagger 6)$.
We don't need to find $0 \dagger 6$ because $x \barwedge y$ depends only on the left operand. Find $0 \barwedge y$ $ 0 \barwedge y = (3)(0)-5$ $ \hphantom{0 \barwedge y} = -5$.